As fuel injection control, conventionally, there has been proposed a feedback control system in which a basic fuel injection quantity is calculated on the basis of an air flow rate obtained from an air flow meter and an oxygen quantity remaining in an exhaust gas is detected by an O.sub.2 sensor so as to correct a fuel quantity to have a desired air fuel ratio with which a three-way catalyst may acts most effectively for purifying the exhaust gas. Further, a function to increase fuel in an accelerating operation has been provided to control the air fuel ratio to be a theoretical value (for example, reference is made to "ENGINE CONTROL", Journal of the Institute of Electrical Engineering of Japan, Vol. 101, No. 12, or "Recent Electronics Car", Journal of the Society of Instrument and Control Engineers, Vol. 21, No. 7). According to such a conventional system, however, it becomes impossible to satisfy the control performance by feedback correction effected through an O.sub.2 sensor, especially in a rapidly accelerating operation, so that the amount of NOx remains large. The main reason for this is that there occur a flow delay of exhaust gas in an exhaust pipe, a time delay in the steps effected in the engine until an exhaust gas is produced, etc., and feedback is effected by observing such phenomena. Alternatively, there has been proposed a method in which correction was made by increasing fuel in rapid acceleration to make the air fuel ratio be a theoretical value. In this method, however, there has been a problem that, even though a desired air fuel ratio could be obtained during acceleration, the fuel quantity became too large after the completion of acceleration so that the exhaust gas might include HC and/or CO because the conversion rate of the three way catalyst with respect to HC and CO (the respective rate with which CO or HC is oxidized to CO.sub.2 or H.sub.2 O or with which NOx is reduced to N.sub.2) was lowered. This was mainly caused by the fact that part of the fuel injected into an intake manifold and adhering to a wall surface of the intake manifold, or the adhered fuel (hereinafter referred to as a "liquid film") was evaporated and sucked into a cylinder together with injected fuel, so that there occurred a disadvantage that the air fuel ratio could not always be kept at a desired air fuel value.